Morgan's family told the Cincinnati Enquirer that he died Sunday at his home in Danville, Calif. Morgan died from a non-specified nerve condition.
"The Reds family is heartbroken," team CEO Bob Castellini said in a statement. "Joe was a giant in the game and was adored by the fans in this city.
"He had a lifelong loyalty and dedication to this organization that extended to our current team and front office staff," Castellini said. "As a cornerstone on one of the greatest teams in baseball history, his contributions to this franchise will live forever. Our hearts ache for his 'Big Red Machine' teammates."
The 10-time All-Star was born in Bonham, Texas. He attended Castlemont High School in Oakland, Calif., and California State University before making his Major League Baseball debut in 1963 for the Houston Colt .45s.
Morgan made the All-Star team twice during his 10-year tenure with Houston, and was was traded to the Reds in 1971. He was selected to the National League All-Star Team for eight consecutive seasons from 1972 to 1979.
He also won back-to-back National League MVP awards in 1975 and 1976, which led the team to championships in both seasons.
Morgan played alongside Pete Rose, Johnny Bench, Tony Perez, Joe Morgan, Dave Concepcion, George Foster, Cesar Geronimo and Ken Griffey Sr., on "the Big Red Machine," a nickname given to the group of players who made up one of the best teams in MLB history.
"Joe wasn't just the best second baseman in baseball history, he was the best player I ever saw and one of the best people I've ever known," Bench in a statement. "He was a dedicated father and husband and a day won't go by that I won't think about his wisdom and friendship.
"He left the world a better, fairer, and more equal place than he found it, and inspired millions along the way."
He had a career .271 batting average and was inducted into the Baseball Hall of Fame in 1990. His 2,649 games played and 268 career home runs are the most in MLB history for a second baseman.
Morgan went on to work as a Reds TV broadcaster in 1985 and a Giants broadcaster for nine years. He then worked as a commentator for 20 years on ESPN's Sunday Night Baseball.
He had served a special advisor for the Reds since 2010. Morgan is survived by his wife, Theresa, and daughters Kelly, Ashley, Lisa and Angela.